a study on the mechanisms of interaction between deep … · 2019. 7. 30. · researcharticle a...

Research ArticleA Study on the Mechanisms of Interaction between DeepFoundation Pits and the Pile Foundations of Adjacent SkewedArches as well as Methods for Deformation Control

Kai Cui ,1 Jun Feng ,2 and Chengyong Zhu2

1Key Laboratory of High-Speed Railway Engineering of the Ministry of Education, Southwest Jiaotong University,Chengdu, Sichuan 610031, China2School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China

Correspondence should be addressed to Jun Feng; [email protected]

Received 21 January 2018; Revised 4 March 2018; Accepted 12 March 2018; Published 17 April 2018

Academic Editor: Changzhi Wu

Copyright © 2018 Kai Cui et al. This is an open access article distributed under the Creative Commons Attribution License, whichpermits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The construction of deep foundation pits is characterized by heavy loads on pile foundations, complex interactions between thefoundation pit and pile foundations, and stringent requirements for deformation control. In thiswork, FLAC3Dwas used to performcomputational analyses on the displacement responses of pile caps and the retaining walls of foundation pits in a variety of casesand reinforcement schemes. The computational results indicate that the piles of skewed arches interact with the retaining walls ofthe foundation pits through soil masses. We also revealed the mechanism by which deep foundation pits interacted with the pilefoundations of adjacent skewed arches. Based on the mechanisms of interaction between foundation pit excavations and the pilesof skewed arches, we proposed three reinforcement schemes for controlling the deformations associated with these interactions.The arched wall reinforcement scheme could provide a satisfactory result in terms of the control of horizontal displacements in thepile foundations and project costs.

1. Introduction

As society continues to grow, municipal projects like sub-ways are becoming increasingly integrated with large publicbuildings. The simultaneous appearance of foundation pitsand pile foundations is thus becoming increasingly proba-ble. However, the excavation of foundation pits will affectadjacent pile foundations via excavation-inducedmovementsin soil mass outside the foundation pit; the sliding soillayers also generate additional displacements and bendingmoments in adjacent piles. Deep foundation pit projectsare characterized by large pile loads, high design risks anddifficulties, complex foundation pit-pile interactions, andstringent demands for deformation control [1–6]. Therefore,it is necessary to conduct studies on the interactions betweenfoundation pits and their adjacent piles, as well as techniquesfor deformation control.

At present, a number of researchers have studied theinteractions of foundation pits with adjacent piles and

obtained several notable results. Du and Yang [7] set upinterfacial sliding blocks between piles and soils and defineda unified ultimate soil resistance for soil masses based onelasticity theory and 𝑝-𝑦 curves; on this basis, Du and Yangscrutinized the plastic yield of soil masses and proposedan elastoplastic solution for the effects of foundation pitexcavations on their adjacent pile foundations. Chen et al.[8] used the Plaxis program to perform two-dimensional(2D) numerical analyses on the processes of foundation pitexcavations with pile-row supports to simulate a number offactors by which foundation pit excavations affected theiradjacent pile foundations. Du and Yang [9] reinforced thepassive zone inside the foundation pits and soil massesoutside of the pit to increase the strength and deformationresistance of soil masses and performed analyses on thereinforcement measures that were taken when excavationsinduced excessively large deformations in adjacent pile foun-dations. Zheng et al. [10] performed measurements duringthe excavation of foundation pits and found that these

HindawiComplexityVolume 2018, Article ID 6535123, 19 pageshttps://doi.org/10.1155/2018/6535123

http://orcid.org/0000-0002-7732-6274

http://orcid.org/0000-0002-8723-0225

https://doi.org/10.1155/2018/6535123

2 Complexity

excavations significantly affected nearby pile foundations.Furthermore, when large gaps were used in the pile-rows,it was found that the horizontal displacement in the water-stopping curtain could exceed that of the pile-rows. Basedon the ABAQUS finite element analysis program, Zhenget al. [11] performed Mohr-Coulomb constitutive modelanalyses on the excavation of foundation pits, thus obtain-ing the subsidences and deformation patterns of pier pilesclose to the foundation pit during these excavations. Gonget al. [12] compared theoretical results with experimentalresults and analyzed how the reduction factor for lateralpile resistance is related to factors such as the excavationdepth of the foundation pit, side length, length-to-widthratio, and pile length. Ong et al. [13] conducted a seriesof centrifuge model tests to investigate the behavior of asingle pile subjected to excavation-induced soil movementsbehind a stable retaining wall in clay. The results reveal that,after the completion of soil excavation, the wall and thesoil continue to move and such movement induces furtherbending moment and deflection on an adjacent pile. Zhanget al. [14] proposed a two-stage analysis method to study thebehavior of pile foundations subjected to excavation-inducedground movements. This method can take the influenceof working loads acting on pile heads into account andovercome some deficiencies of existing methods. Then, theproposed method is verified by comparing the calculatedresults with boundary element solutions and centrifuge testdata. Lee [15] built a three-dimensional numerical model tostudy the behavior of a single pile and adjacent tunnelingexcavation in the lateral direction. The numerical analysesincluded comparisons between the current study, previouselastic solutions, and advanced 3D elastoplastic analyses.Bilotta and Russo [16] computed the effectiveness of asimple row of piles induced by the tunneling excavationby means of three-dimensional finite element analyses, thusallowing for an investigation of the relationship betweenperformance and simple geometrical parameters. The resultsof centrifuge testing were reported and used as a benchmark.The potential damage has been quantified in this work, takinginto account both the settlement profile and the horizon-tal strain induced at the ground surface by the tunnelingexcavation.

As shown in Figure 1(a), this study targeted the foun-dation pit of the Shuangliu airport (T2 Terminal) station(a railway station in Chengdu, China) with a length ofabout 980m, and its maximum excavation depth and widthare 22m and 57m, respectively. The length of the subwayfoundation pit within the area of the skewed arch pile caps ofthe airport terminal is almost 600m long, and the clearancebetween the foundation pit and the pile foundations is only12m. There are 16 skewed arch piles on the side of theterminal facing the subway station, and the dimensions ofeach pile cap are 20m × 20m × 3.5m. There are 15 manuallydrilled piles under the pile caps, and these bear the loadsof the skewed arch structure of the terminal. The standardload values of the skewed arch are as follows: a horizontalreaction of 12,160 kN, a vertical force of 11,200 kN, and abendingmoment of 23,980 kN⋅m.The permissible horizontaldeformation in each pile cap is ≤8mm. This project is

characterized by large loads on the piles of the skewed arches,complex interactions between the subway foundation pit andthe terminal pile foundations, stringent deformation controlrequirements, and high levels of difficulty in the design andconstruction of the pit foundation itself.

Though the above previous researches fully studied theinfluence of foundation pit excavation on the deformationof pile foundation, a lot of experience has been gained indesign and construction of foundation pit. However, deepfoundation pit does not appear often at the same timewith inclined arch group pile foundation, which is the caseof Shuangliu airport station. As the clearance between thefoundation pit and the skewed arch terminal piles is smalland the horizontal reaction transferred by the skewed archstructure onto its pile foundations is large, the excavationof the deep foundation pit and the loading of the skewedarch piles will inevitably interact with each other. Hence,an understanding of the mechanisms of interaction betweenthese structures is a necessary basis for the design of defor-mation control measures. In the present literature, analyseson the mechanisms of interaction of these structures andstudies on the control of their deformations are ratherscarce.

In summary, numerical analysis was used in this workto study the mechanisms of interaction between the piles ofskewed arches and deep foundation piles and techniques forthe control of deformations associated with these interac-tions. The findings of this study can be directly applied to theconstruction design of subway foundation pits.

2. Numerical Analysis onthe Impacts of Deep Foundation PitExcavations on the Deformations ofSkewed Arch Pile Foundations

2.1. Computational Domain and Loads. FLAC3D was usedto compute the effects of the excavation and reinforcementprocesses of the deep foundation pit on the pile foundationsof the skewed arches. A strip of soil between two skewedarch pile caps in a central area of the airport was selectedas the focus for this study, as shown in Figure 1(a). One ofthese skewed arch pile caps was selected as the subject of oursimulations. The excitation loads are shown in Figure 1(b);the horizontal reaction was 12,160 kN, the vertical force was11,200 kN, and the bending moment was 23,980 kN⋅m.

2.2. Computational Model. Because FLAC3D directly con-structs finite differences in its computations (unlike the CAEprogram), its three-dimensional (3D) mesh is constructedaround the geometry of the actual physical object [17–21].However, the preprocessing of complex grids in FLAC3Dis somewhat inadequate, as a result. Therefore, the physicalmodel in the computational domain was modeled usinghexahedral meshing in ANSYS. Data interface programswere then used to import the ANSYS element and nodedata into FLAC3D. As shown in Figure 2(a), beam elements(BEAM structural unit) were used to simulate the 1st- and2nd-row concrete cross supports, 3rd- and 4th-row steelsupports, the support column bearing the four rows of cross

Complexity 3

Inclined arch pilefoundation

Parking lot

Shuangliu airport station

T2 terminal

Research area

(a) Schematic diagram of the computational domain

Station foundation tip

Reinforcement measures

Inclined arch pile foundationA B C E F G H

200 200 200

200 20010000 10000

Fz = 11200 kN

My = 23980 kN·m

Fx = 12160 kN

D

(b) Force diagram of the computational domain

Figure 1: Schematic diagram and force diagram of the computational domain.

Uplift pile

Steel support

concrete support

Link rod

Lattice column

(a) Local structural element

Z GroupGroup Slot: 1

soil 1leftwallrightwallcapsoil 2pilesoil 3soil 4

Enclosure wall Inclined arch pile

Soil-fillingClay

Pebble soil

Mudstone

(b) Finite element model

Figure 2: Finite element model of the station foundation pit.

supports, and the tie-rods connecting the 3rd- and 4th-rowsteel supports. Because an appropriate stiffness parametercould not be determined for the pile elements in FLAC3D(PILE structural unit) and because the tension piles at thebottom of the pit are not the main focus of this study,the tension piles at the bottom of the pit were simulatedusing beam elements to simplify the computational model.Based on the principles of bending stiffness equivalence,the retaining piles on either side of the foundation pit werereduced to a solid continuous underground concrete wall.The skewed arch pile foundations were simulated using solidmesh elements. In FLAC3D, bending moments cannot bedirectly applied onto mesh nodes, which is necessary forsimulating the loads borne by the pile cap of the skewedarch piles. Therefore, a short vertical beam with sufficientstiffness was set in the pile cap during the modeling, whichis rigidly connected to the solid elements of the pile cap. Thisis similar to welding the short beam to the pile cap, whichis largely consistent with actual scenarios. In this way, forcesand bending moments can be applied onto the top nodeof the short beam, thus circumventing the need to equateforces to bending moments via the equivalence of forces.Constraints were applied in directions corresponding to thefour lateral sides and bottom of the model; since FLAC3Duses Newton’s Laws, we effectively constrained the nodevelocities on each of these surfaces. During the modeling of

structural elements, the connections between different struc-tural elements were handled using shared nodes. However,there are slight discrepancies between this method and actualscenarios; for example, lattice columns should be connectedto steel supports through hinged joints, and the connectionof tie-rods to steel supports should be similarly mediated byhinged joints, whereas the tension piles and support pillarsshould be connected via rigid connections. Nonetheless,the simplification of these connections will not significantlyaffect the overall computational results of extremely largemodels.

In order to reduce the influence of boundary constraintson the calculated stress field, the influence area of deepfoundation pit is controlled by the depth of the hard soilbehind the wall. The model range is 140m (length—𝑥direction) × 34.6m (width—𝑦 direction) × 70m (height—𝑧direction). The number of units (element) is 77056, andthe number of nodes is 82940. The retaining wall and soilare connected using the common node connection, inclinedarch pile and soil node connection, steel support, reinforcedconcrete support, and pile and implantable structural unitsimulation (embedded). In FLAC3D, the degree of freedomof the unit and the soil automatically couple.

Based on the methods described above, we obtained afinite element model for the subway foundation pit, as shownin Figure 2(b). We then assigned attributes and sectional

4 Complexity

Table 1: Material attributes and sectional characteristics of the structural elements.

Parameter 1st- and 2nd-rowconcrete supports

3rd- and 4th-row steelsupports

Tension piles at thebottom of the pit Lattice columns Tie-rods Units

Elastic modulus 32500 206,000 30000 206000 206000 MPaPoisson’s ratio 0.20 0.26 0.20 0.26 0.26 —Moment of inertia inthe 𝑦-axis, 𝐼𝑦

0.0427 0.00131 0.102 0.00299 0.00035 m4

Moment of inertia inthe 𝑧-axis, 𝐼𝑧

0.0667 0.00131 0.102 0.00089 0.0017 m4

Polar moment ofinertia, 𝐽 0.1094 0.00262 0.204 0.00388 0.00205 m4

Cross-sectional area,A 0.80 0.0298 1.131 0.0636 0.0168 m2

characteristics to the structural elements of the finite elementmodel, as shown in Table 1. FLAC3D is a 3D finite differenceprogram that was specifically developed for rocks and soilmasses and therefore has extremely detailed settings in itsconstitutive soil models. The Mohr-Coulomb elastoplasticmodel can be used formost rock and soil engineering studies,and the parameters of these models are usually relativelyeasy to obtain. Therefore, soils with weaker levels of strengthin the finite element model were modeled using the Mohr-Coulomb elastoplastic constitutive model. Chengdu clayswere defined with a density of 1.98 g/cm3, cohesion of 35 kPa,internal friction angle of 12∘, elastic modulus of 7.2MPa, andPoisson’s ratio of 0.35. Gravelly soils were assigned a densityof 2.20 g/cm3, internal friction angle of 40∘, elastic modulusof 35MPa, and Poisson’s ratio of 0.29. The mudstones in themodel have a density of 2.20 g/cm3, internal friction angleof 55∘, elastic modulus of 400MPa, and Poisson’s ratio of0.30.

2.3. Computational Procedure

Step 1. The tension piles on the bottom of the pit, latticecolumns, retaining walls, and skewed arch piles were assem-bled first. In terms of FLAC3D procedures, this correspondsto the setting of material attributes and the assembly ofstructural elements in the soil mass model, followed by around of equilibration. The initial in situ stresses of the soilswere then calculated.

Step 2. The initial displacements produced by the initialstresses of the soil masses were reset, and excavation wasperformed up to 0.8m below the surface, followed by equi-libration.

Step 3. The 1st-row horizontal supports were mounted 0.5mbelow the surface, followed by equilibration.

Step 4. The excavation was extended to 7.8m below the sur-face, and partial stress release was performed over 1,000 iter-ations.The 2nd-row horizontal supports were then mounted,followed by equilibration.

Step 5. The excavation was extended to 12.3m below thesurface, followed by partial stress release over 1,000 iterations.

Horizontal displacement detection lineA

B

C

D

E

Figure 3: Displacement monitoring points on the skewed arch pilefoundation and retaining walls.

The 3rd-row horizontal supports and tie-rods connected tothese supports were then mounted, and the model was thenequilibrated.

Step 6. The excavation was extended to 16.8m below thesurface, followed by partial stress release over 1,000 iterations.The 4th-row horizontal supports and their associated tie-rodswere then mounted, and the model was equilibrated.

Step 7. The excavation was extended to 20.3m below the sur-face, followed by equilibration. At this point, the excavationof soil masses for the foundation pit has been completed.

Step 8. The displacement data generated by the excavationswere zeroed, and loads were applied onto the skewed archpile foundations. A horizontal force of𝐹𝑥 = 12,160 kN, verticalforce of 𝐹𝑧 = 11,200 kN, and bending moment of 𝑀𝑦 =23,980 kN⋅m were applied on the central node of the uppersurface of the pile cap. The model was then equilibrated.

2.4. The Layout of Monitoring Points. Prior to the numericalcomputations, the (four) corners and central point of thepile cap were set as monitoring points for displacement, asshown in Figure 3. The mesh nodes on two 𝑦 = 20 straightlines on the left and right retaining walls were selected asmonitoring points for horizontal displacement. This setupallows for a detailed study on the displacement responses ofthe pile cap and retaining walls. The A and D monitoringpoints correspond to pile cap corners closer to the foundationpit, and the AD side is parallel to the 𝑦-axis of the modelcoordinate system.

Complexity 5

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−1.5143E − 02−1.5000E − 02−1.4500E − 02−1.4000E − 02−1.3500E − 02−1.3000E − 02−1.2500E − 02−1.2000E − 02−1.1500E − 02−1.1000E − 02−1.0500E − 02−1.0000E − 02−0.9500E − 02−0.9000E − 02−0.8500E − 02−0.8000E − 02−0.7500E − 02−0.7000E − 02−0.6500E − 02−0.6257E − 02

Figure 4: Contour maps of the pile cap horizontal displacement in each case.

−1.1646E − 03−1.1500E − 03−1.1250E − 03−1.1000E − 03−1.0750E − 03−1.0500E − 03−1.0250E − 03−1.0000E − 03−9.7500E − 04−9.5000E − 04−9.2500E − 04−9.0000E − 04−8.7500E − 04−8.6383E − 04

−3.4284E − 03−3.2500E − 03−3.0000E − 03−2.7500E − 03−2.5000E − 03−2.2500E − 03−2.0000E − 03−1.7500E − 03−1.5000E − 03−1.2500E − 03−1.0000E − 03−7.5000E − 04−7.1133E − 04

−3.4877E − 03−3.2500E − 03−3.0000E − 03−2.7500E − 03−2.5000E − 03−2.2500E − 03−2.0000E − 03−1.7500E − 03−1.5000E − 03−1.2500E − 03−1.0000E − 03−7.5000E − 04−6.8456E − 04

−3.9754E − 03−3.7500E − 03−3.5000E − 03 −3.2500E − 03−3.0000E − 03−2.7500E − 03−2.5000E − 03−2.2500E − 03−2.0000E − 03−1.7500E − 03−1.5000E − 03−1.2500E − 03−1.0000E − 03−7.5000E − 04−6.6823E − 04



Horizontal displacement/uxHorizontal displacement/ux Horizontal displacement/ux


Figure 5: Contour maps of the pile cap vertical displacement in each case.

3. Computational Analysis of the Skewed ArchPile Foundations prior to Reinforcement

3.1. The Displacement Responses of the Pile Cap. Based on theresults of the numerical calculations, the horizontal and ver-tical displacements of the skewed arch piles were describedusing contour maps. To facilitate the discrimination of thecontour maps, the mesh outlines are not shown when thehorizontal displacement is shown, as is the case in Figures4 and 5. In Figures 4 and 5, the images from left to rightcorrespond to Cases 1–6. In Case 1, the excavation reached0.8m below the surface, and the 1st-row horizontal concrete

supports have been mounted. In Case 2, the excavationhas progressed to 7.8m below the surface, and the 2nd-rowhorizontal concrete supports have been mounted. In Case 3,the excavation has reached 12.3m, and the 3rd-rowhorizontalsteel supports and tie-rods have been mounted. In Case 4,the excavation is 16.8m below the surface, and the 4th-rowhorizontal steel supports and tie-rods have been mounted. InCase 5, the excavation has been completed (the excavation hasreached 20.3m below the surface, which is the bottom of thefoundation pit). In Case 6, loads have been applied onto theskewed arch pile foundations (the displacements caused bythe excavation have been zeroed).The horizontal and vertical

6 Complexity

Table 2: The horizontal and vertical displacements of the pile cap in each case.

Monitoring points CasesCase 1 Case 2 Case 3 Case 4 Case 5 Case 6

Horizontal displacement

Corner A 0.081 0.64 1.20 3.48 3.76 14.88Corner B 0.093 0.7 2.07 3.56 3.86 15.06Corner C 0.093 0.7 2.08 3.57 3.87 15.14Corner D 0.081 0.64 1.20 3.48 3.77 14.95Corner E 0.086 0.67 2.03 3.52 3.82 14.80

Vertical displacement

Corner A 0.89 0.75 0.59 0.70 1.15 10.83Corner B 1.16 3.43 3.49 3.97 5.08 3.04Corner C 1.15 3.39 3.45 3.94 5.05 3.21Corner D 0.87 0.71 0.55 0.67 1.12 10.96Corner E 1.04 2.13 2.11 2.42 3.20 7.83

displacements in the skewed arch pile foundations at eachmonitoring point corresponding to each case are shown inTable 2.

In Table 2, it is shown that A and D, which lie on the pilecap side closer to the foundation pit, have slightly smallerhorizontal displacements compared to B and C, which areon the opposite side. This is because the displacements ofthe pile cap on the side closer to the foundation pit arerestricted by retaining piles. Furthermore, the retaining pileshave been reinforced in a timely manner in each excavationstep, which subsequently restricts soil mass displacementsbetween the pile cap and the retaining piles; however, thesoil masses on the opposite side do not have any additionalrestraints.Therefore, the displacements of the pile cap cornerson the side closer to the foundation pit are slightly lowerthan those on the opposite side, both during the excavationprocess and after the application of loads onto the pile cap.However, the data in Table 2 indicates that the differencesbetween the horizontal displacements of the corners are verysmall. This is because the skewed arch pile foundations aresubstantially stiffer than the soil masses, and the formermay be approximated as a rigid body. As a whole, thehorizontal motions of the pile cap may be approximatedas the movements of a rigid body. Furthermore, based onthe changes in displacement in each excavation step, thehorizontal displacements caused by the excavation of thefoundation pit are quite small, even without any furtherreinforcement. By the end of the excavation, the cumulativehorizontal displacement was only 3.8mm or so (the centralpoint of the pile cap, E, is the reference in this case).Nonetheless, the application of loads onto the skewed arch’spiles (including a horizontal force, vertical force, and bendingmoment) induces a horizontal displacement of 14.8mm.Thisdisplacement is enough to undermine the stability of theupper structures of the terminal. Therefore, it is necessary toreinforce the soil masses between the foundation pit and theskewed arch pile foundations.

Table 2 also indicates that the vertical displacementsof A and D are slightly lower than those of B and C.Significant differences in subsidence were generated betweenthese corners with increasing excavation depth. The verticaldisplacement of the central point of the pile cap is essentially

equivalent to the average vertical displacement of the fourcorners. The displacements of the pile cap side closer tothe foundation pit are restricted by retaining piles, and theretaining piles are always reinforced in a timely manner ineach excavation step, thus constraining the displacementsof the strip of soil between the retaining piles and pilecap. However, the soil masses on the other side of the pilecap have no additional restraints. Therefore, the pile capcorners on the side adjacent to the foundation pit alwayshave smaller vertical displacements than pile cap corners onthe opposite side, both during the excavation process andafter the application of loads onto the pile cap. However,upon the application of loads, the vertical displacementtrends are completely reversed, as the pile cap corners onthe side adjacent to the foundation pit have much greatersubsidences than those of the opposite side. This is becausethe pile cap’s displacements under the actions of the threeaforementioned forces rotate in an anticlockwise directionaround an axis parallel to the 𝑦-axis; consequently, there arehighly significant differences in the subsidences of the pilecap’s corners after loads have been applied. This is extremelylikely to be detrimental for the stability of the upper structuresof the terminal. Hence, it is necessary to reinforce the soilmasses between the foundation pit and the pile foundationsof the skewed arch.

3.2. The Displacements and Stress Responses of the RetainingWalls of the Foundation Pit. The horizontal displacements ofthe retaining wall monitoring points farther and closer tothe pile foundations were extracted, as shown in Figure 6.In this figure, it is shown that the deformation state of theretaining walls of the foundation pit is generally consistentwithType 3 displacement state curves, prior to the applicationof loads onto the pile foundations of the skewed arch. Afterloads were applied onto the skewed arch piles, the horizontaldisplacements of the retaining wall closer to the piles exhibita linear distribution along the wall, in the vertical direction,with the displacement being greatest at the top of the wall.This is because extremely large loads were applied at thecentral point of the upper surface of the pile cap. Uponthe application of loads onto the skewed arch piles, thefoundation pit retaining walls farther from the piles are

Complexity 7

−30

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0−6 0 6 12 18

case 1case 2case 3

case 4case 5case 6

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l Dep

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(m)

Horizontal Displacement ux (mm)

(a)

case 1case 2case 3

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l Dep

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Figure 6: Horizontal displacements of the monitoring points on the retaining wall that are farther and closer to the pile foundations.

restrained by the retaining wall closer to the piles. Becauseaxial forces and displacements are transferred to the fartherretaining wall via horizontal supports, the distributions of itshorizontal displacements are exactly opposite to that of thecloser retaining wall: the displacements at the top of the wallare small, but large at the bottom.

4. Computational Analysis on the ReinforcedSkewed Arch Pile Foundations

4.1. Analyzing the Effects of Reinforcement via Isolation Pilesand Jet-Grouted Piles (1st Reinforcement Scheme)

4.1.1. Reinforcement Scheme. To ensure the safety of the ter-minal pile caps, soil reinforcement was performed on theretaining piles on the right side of the airport station andbetween the pile caps of the terminal; this reinforcementwas performed via a combination of isolation piles and jet-grouted piles. Two rows of isolation piles were used, and thepile-rowswere located 2.1m from the edges of the pile cap; thediameter of the jet-grouted piles was 800mm. Zones A andB were defined according to the reinforcement requirementsof the area. Zone A was reinforced with a pile overlap of10 cm, while Zone B was reinforced using a plum-shapedarrangement with a 1.4m gap, as shown in Figure 7.

The parameters of the isolation piles were as follows:pile diameter = 1,500mm, interpile gap = 2.9m, pile length

= 20m, and absolute elevation of the top of the piles =491.4m. The range of reinforcement and requirements ofthe jet-grouted piles were as follows: all of the upper soilmasses needed to be reinforced; the slightly compacted gravelsoils in which the piles were embedded are not smaller than1m, and the length of the piles was approximately 7–9m.During the construction, the pile lengths were determinedaccording to the in situ geological conditions. Plate girders,whose sectional dimensions are 4.4m ∗ 0.6m, were set upon top of the piles. The absolute elevation of the plate girderswas 491.9m, and they were set in a longitudinal layout. Thereinforcement requirements of the soil masses are describedas follows: after reinforcement, the deformation moduli ofthe soil masses in Zone A and Zone B must be not lessthan 80MPa and 20MPa, respectively. During the numericalcalculations, these deformation moduli were taken as theelastic moduli of the soil masses in Zones A and B, to ensurethat the calculations lean towards conservative estimates. Afinite element model of the reinforced subway foundationpit was constructed based on this reinforcement scheme, asshown in Figure 8.

4.1.2. The Displacement Responses of the Pile Caps. Thehorizontal and vertical displacements of the skewed archpile foundations in each construction case are shown inFigures 9 and 10. After reinforcement, the horizontal andvertical displacements of the pile caps gradually increase

8 Complexity

Foundation ditch

B area

A area

Analysis area

5.26 1626 27 2831

32 3616 16 16

8 8

20 10 18 14 18

7.4 7.4

17.45 17.45 72.01

1.9

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18

Enclosure wall

(a) Schematic diagram of the areas for soil mass reinforcement

Inclined arch cap of T2 terminal12

Isolated pile

Region A7.75

2.9

2.9

2.1

2.9

2.75

6.89 Region B

Diameter 1500 mm

Rotary churning pile, diameter 800 mm

1.4

1.4

1.4

1.4

Occlusion 0.1m

(b) Details of the reinforcement of Zones A and B

Figure 7: Schematic diagram of the isolation pile + jet-grouted pile reinforcement scheme.

Reinforcement area BReinforcement area A

Reinforcement area A

Enclosurewall

17.45 17.45

3.5

18 14 18

7

7.4 7.4

Reinforcement area B

Z GroupGroup slot: 1soil 1leftwallbregionaregionrightwallmidwallcapsoil 2pilesoil 3soil 4

Tran

sfer c

hann

el

Figure 8: Finite element model of the reinforced subway foundation pit.

with each excavation step. At the end of the excavation, thehorizontal and vertical displacements at the center of the pilecap were 2.92mm and 1.04mm. This corresponds to 24%and 68% reductions in horizontal and vertical displacement,respectively, as compared to the unreinforced model. Basedon the impacts of the foundation pit excavation on the

horizontal displacement of the skewed arch pile foundations,the reinforcement effect is more obvious. Upon loadingof these piles, the horizontal and vertical displacementsat the center of the pile cap increased to 6.03mm and4.03mm, respectively. Compared to the unreinforced model,the horizontal displacement decreased by 59% while the

Complexity 9

−1.3238E − 04−1.2500E − 04−1.0000E − 04−7.5000E − 05−5.0000E − 05−2.5000E − 050.0000E + 000.0000E − 054.7500E − 054.5000E − 054.2500E − 044.0000E − 04

−2.5803E − 03−2.5000E − 03−2.2500E − 03−2.0000E − 03−1.7500E − 03−1.5000E − 03−1.2500E − 03−1.0000E − 03−7.5000E − 04−5.0000E − 04−2.5000E − 040.0000E + 002.5000E − 043.0600E − 04

−4.6205E − 03−4.5000E − 03−4.2000E − 03−4.0000E − 03−0.7500E − 03−0.6000E − 03−0.2500E − 03−0.0000E − 03−2.7500E − 03−2.6000E − 03−2.5000E − 03−2.2500E − 03−1.7500E − 03−1.5000E − 03−1.2000E − 03−1.0000E − 03−7.5000E − 04−5.0000E − 04−0.7972E − 04

−7.0074E − 03−7.0000E − 03−6.5000E − 03−6.0000E − 03−5.5000E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03−3.5000E − 03−3.0000E − 03−2.5000E − 03−2.0000E − 03−1.9492E − 03

−0.5100E − 03−0.5000E − 03−0.6000E − 03−7.5000E − 03−7.0000E − 03−6.5000E − 03−6.0000E − 03−5.5000E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03−3.5000E − 03−3.0000E − 03−2.5000E − 03

−6.9000E − 03−6.7500E − 03−6.5400E − 03−6.3500E − 03−6.0000E − 03−5.7500E − 03−5.5000E − 03−5.2500E − 03−5.0000E − 03−4.7500E − 03−4.5000E − 03−4.2500E − 03−4.0000E − 03−3.7500E − 03−3.5000E − 03


Horizontal displacement/uxHorizontal displacement/ux Horizontal displacement/ux

Figure 9: Contour maps of the horizontal displacements in each case.

4.3470E − 055.0000E − 057.5000E − 051.0000E − 041.2500E − 041.5000E − 041.7500E − 042.0000E − 042.2500E − 042.5000E − 042.7500E − 043.0000E − 043.1674E − 04

−1.3790E − 03−1.2500E − 03−1.0000E − 03−7.5000E − 04−5.0000E − 04−2.5000E − 040.0000E + 002.5000E − 045.0000E − 047.5000E − 041.0000E − 031.2500E − 031.5000E − 031.7500E − 032.0000E − 032.2500E − 032.5000E − 032.7500E − 032.7456E − 03

−1.9705E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 005.0000E − 041.0000E − 031.5000E − 032.0000E − 032.5000E − 033.0000E − 033.1881E − 03

−2.9114E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 005.0000E − 041.0000E − 031.5000E − 032.0000E − 032.5000E − 032.6941E − 03

−2.7000E − 03−2.5000E − 03−2.0000E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 005.0000E − 041.0000E − 031.5000E − 032.0000E − 032.1305E − 03

−4.0170E − 03−4.7100E − 03−4.5000E − 03−4.2500E − 03−4.0000E − 03−3.7500E − 03−3.5000E − 03−3.2500E − 03−3.0000E − 03−2.7500E − 03−2.5000E − 03−2.2500E − 03−2.0000E − 03−1.7100E − 03−1.5000E − 03−1.2400E − 03

Vertical displacement/ux Vertical displacement/uxVertical displacement/ux

Vertical displacement/ux Vertical displacement/ux Vertical displacement/ux

Figure 10: Contour maps of the vertical displacements in each case.

vertical displacement decreased by 49%. It is shown that thereinforced zones have had a significant effect on restrainingthe horizontal displacements of the pile cap, especially afterthe loads were applied. Despite the conservative estimatesof this computation, this reinforcement scheme has met thestability requirements of the upper structures of the terminal.Therefore, it is reasonable to postulate that this zonal rein-forcement scheme will meet the safety requirements of theengineering applications.

4.1.3. The Displacement Responses of the Foundation Pit’sRetaining Walls. The horizontal displacements extractedfrom the monitoring points on the retaining walls fartherand closer to the pile foundations are shown in Figure 11.In this figure, it is shown that the maximum displacementin the retaining walls always occurs near the bottom of theexcavated surface during the excavation process (in whichinternal reinforcement was added after each excavationstep). Furthermore, these displacements generally increase

10 Complexity

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case 1case 2case 3

case 4case 5case 6

Wal

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Wal

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case 1case 2case 3

case 4case 5case 6

(b)

Figure 11: The horizontal displacements of the monitoring points on the retaining walls farther and closer to the pile foundations.

with increasing excavation depth. However, the displace-ments of the retaining wall farther from the skewed archfoundation piles exhibit a parabolic trend with respect todepth. The retaining wall closer to the foundation pilesdoes not exhibit significant fluctuations in its horizontaldisplacements, because its displacements are restricted by theretaining walls of the transfer channel area. According to thedeformation law of the whole wall, the numerical calculationis basically consistent with the displacement change law of thefield monitoring.

4.2. Analyzing the Effects of Arched Wall Reinforcement (2ndReinforcement Scheme). Here, we propose the installation ofarched walls between the skewed arch pile foundations andthe foundation pit retaining walls to reduce project costsand control the horizontal displacements of the skewed archpiles. The effects of this method are analyzed in this section.It is well understood that arched structures have excellentspanning capabilities and are mechanically sound. As theapplication of external loads on arched structures mainlyresults in compressive forces, the bending deformations ofits members are generally quite small. The construction ofarched structures using materials with high compressivestrengths will contribute to the strengths of these materials.However, horizontal reactions will be generated around theabutments of an arched structure, and these reactions are verylargewhen the span is large.These forces are both difficult andcostly to deal with. Therefore, it is necessary to pay attention

to the handling of the foot of the arch during the selection ofarched structures.

4.2.1. Selection of an Arched Structure. To understand themechanical characteristics of different arch structures fromthe perspective of structural stresses, we selected archedwall structures that are suitable for 3D numerical analysis.Using ANSYS, we analyzed the mechanical characteristics ofa parabolic arch and an arc-shaped arch that have the samespan and arc height, and a parabolic arch with the same archeight but different span. Concrete was used as the materialof these structures, and the sections are arched wall sectionsof unit height. In the structural analysis, if we assume that theheight of the arched wall is 5m and the 12,160 kN horizontalforce acting on the skewed arch pile foundations is uniformlyapplied across the crown of the arched wall, the force sharedby a unit height of the arched wall is then 20% of the totalforce (2,432 kN).This was used to construct the finite elementmodel of the arched walls’ member systems. The contourmaps of the bending moments, shear forces, and axial forcesthat were computed for the three aforementioned archedstructures are shown in Figure 12. The bending moments,shear forces, and axial forces that were extracted from thekey positions of each arched structure are shown in Table 3.In Table 3, it may be inferred that a parabolic arch performsbetter than an arc-shaped arch.

4.2.2. Displacement Response of the Pile Cap. A parabolicarched structure was used to reinforce the foundation pit of

Complexity 11

−0.1

20E

+ 0

7

−0.6

69E

+ 0

6

0.40

2E +

06

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+ 0

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+ 0

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+ 0

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−0.1

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+ 0

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+ 0

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+ 0

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+ 0

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+ 0

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+ 0

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−0.1

35E

+ 0

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−0.1

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(a)

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+ 07

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+ 06

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+ 0

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+ 0

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+ 0

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+ 0

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+ 0

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+ 0

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+ 0

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(b)

−0.1

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+ 0

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+ 0

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+ 0

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−0.9

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+ 0

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+ 0

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+ 0

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+ 0

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+ 0

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+ 0

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+ 0

7

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+ 0

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0.39

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06

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+ 0

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+ 0

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+ 0

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+ 0

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0731

E +

06

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−0.4

31E

+ 0

6

0.34

6E +

06

0.11

2E +

07

0.18

9E +

07

(c)

Figure 12: Force contour maps of three different arched structures (a, b, and c are the bending moments, shear forces, and axial forces of thecircular curve, Type I parabola, and Type II parabola).

Table 3: Forces calculated at the key positions of each arched structure.

Curve typeQuantity

Vertical displacement at the crown (mm) Bending moment (kN⋅m) Shear force (kN) Axial force (kN)Crown Foot Crown Foot Crown Foot

Circular arc 27.8 5370 3824 1205 982 1122 1320Parabola

Type I 8.9 3681 1738 1194 418 1106 1573Type II 3.6 2669 1107 1194 290 766 1389

the station. The arched wall was constructed using concreteand links the retaining walls of the foundation pit to the pilesof the skewed arch. A block that conforms to the curve of thearch was set between the crown and the pile foundations toconnect these structures.The block was constructed from thesame materials as the arched wall and has the same depth asthat of the wall, as shown in Figure 13.

To investigate the effects of reinforcement using archedwallswith different heights, we performednumerical analyseson three archedwall heights, using the same construction sce-nario.The dimensions of the arched walls were as follows: thefirst arched wall had a height of 5.15m, and the coordinatesof the top and bottom of this wall were 𝑧 = −0.8m and 𝑧

= −5.95m, respectively. The second arched wall was 9.25mhigh, and the coordinates of the top and bottom of this wallwere 𝑧 = −0.8m and 𝑧 = −10.05m, respectively. The thirdarched wall was 13.2m high, and the coordinates of the topand bottom of this wall were 𝑧 = −0.8m and 𝑧 = −14.0m,respectively.

We calculated the vertical and horizontal displacementsof these arched walls after excavation was completed (i.e.,postexcavation) and after loads were applied on the skewedarch pile foundations (i.e., postloading), as shown in Figures14 and 15. The contour maps illustrating the postexcavationand postloading patterns of horizontal and vertical displace-ment transfer for each arched wall height are shown in

12 Complexity

Group Slot 1soil1leftwallrightwallgqwalltopcapsoil2pilesoil3soil4gqwall Local grid magnification

Z Group

Figure 13: Finite element model of the subway foundation pit after reinforcement using an arched wall.



−8.0023E − 03−7.7500E − 03 −7.2500E − 03−6.7500E − 03−6.2500E − 03−5.7500E − 03−5.2500E − 03−4.7500E − 03−4.2500E − 03−3.7500E − 03−3.2500E − 03−3.1620E − 03


−9.4827E − 03−9.0000E − 03−8.5000E − 03−8.0000E − 03−7.5000E − 03−7.0000E − 03−6.5000E − 03−6.0000E − 03−5.5000E − 03−5.0000E − 03−4.5000E − 03−4.0728E − 03

−5.0000E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03−3.5000E − 03−3.0000E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 04

5.0000E − 047.0752E − 04

−2.6498E − 03−2.5000E − 03−2.2500E − 03−2.0000E − 03−1.7500E − 03−1.5000E − 03−1.2500E − 03−1.0000E − 03−0.7500E − 04−0.5000E − 04−0.2500E − 04

2.5000E − 045.0000E − 047.5000E − 041.0000E − 031.2500E − 031.3581E − 03

−3.1187E − 03−3.0000E − 03−2.7500E − 03−2.5000E − 03−2.2500E − 03−2.0000E − 03−1.7500E − 03−1.5000E − 03−1.2500E − 03−1.0000E − 03−7.5000E − 045.0000E − 042.5000E − 04

2.5000E − 045.0000E − 047.5000E − 041.0000E − 031.2500E − 031.2578E − 03

0.0000E · 00

0.0000E · 000.0000E · 00

Arch wall height H = 13.2 mArch wall height H = 9.25 mArch wall height H = 5.15 m

Figure 14: Contour maps of the postexcavation pile cap displacements in each scenario.

Figures 16 and 17. It is shown that increases in the height of thearched wall reduce the lateral displacements of the pile cap.When the depth of the arched wall was 13.2m, the horizontaldisplacement caused by loading of the skewed arch pilefoundations was only 6.44mm.This is almost the same as thehorizontal displacement that was observed with the isolationpile + jet-grouted pile reinforcement, which was 6.03mm.The difference in displacement between these reinforcementschemes is only 0.41mm. In terms of vertical displacements,the difference between the two reinforcement schemes is only0.5mm. Hence, arched wall reinforcement has effectivelycontrolled the horizontal and vertical displacements of thepile cap. A comparison between the reinforcement effects ofthe arched walls with different heights quickly reveals thatan arched wall height of 13.2m produces the best results.In terms of the control of horizontal displacements in theskewed arch piles, the effectiveness of the 13.2m arched wallis comparable to that of the isolation pile + jet-grouted pilereinforcement scheme.

4.2.3. The Displacement Responses of the Foundation Pit’sRetaining Walls. Under the reinforcement of three differ-ent height arch walls, the horizontal displacements of themonitoring point of retaining wall both far away from pilefoundation and adjacent to pile foundation are shown inFigure 18. In this figure, it is shown that increases in archedwall height decrease the horizontal displacements of theretaining wall closer to the piles (left figures) and have noeffect on the retaining wall far away from the piles. However,the height of the arched wall does not significantly affect theretaining walls (only 2mm), as its effects mainly manifest inthe control of the pile foundation displacements.

4.2.4. Mechanical Responses of the Arched Wall. The contourmaps of the principal stresses and displacements of a 5.15mhigh arched wall are shown in Figures 19, 20, and 21,respectively. It is shown that the archedwall is highly effective,as the principal stresses of the wall mostly act in the samedirection as the tangential lines of the arch curvature. In other

Complexity 13

−9.1200E − 03−9.0023E − 03−8.7500E − 03 −8.5000E − 03−8.2500E − 03−8.0000E − 03−7.7500E − 03−7.5000E − 03−7.2500E − 03−7.0000E − 03−6.7500E − 03−6.5000E − 03−6.2500E − 03−6.0000E − 03−5.7500E − 03−5.5000E − 03−5.2500E − 03−5.0000E − 03−4.9674E − 03

−7.7036E − 03−7.5000E − 03−7.2500E − 03−7.0000E − 03−6.7500E − 03−6.5000E − 03−6.2500E − 03−6.0000E − 03−5.7500E − 03−5.5000E − 03−5.2500E − 03−5.0000E − 03−4.7500E − 03−4.5770E − 03

−6.8602E − 03−6.7500E − 03−6.5000E − 03−6.2500E − 03−6.0000E − 03−5.7500E − 03−5.5000E − 03−5.2500E − 03−5.0000E − 03−4.7500E − 03−4.5000E − 03−4.2500E − 03−4.2027E − 03

−5.8690E − 03−5.8000E − 03−5.7000E − 03 −5.6000E − 03−5.5000E − 03−5.4000E − 03−5.3000E − 03−5.2000E − 03−5.1000E − 03−5.0000E − 03−4.9000E − 03−4.8000E − 03−4.7000E − 03−4.6000E − 03−4.5000E − 03−4.4000E − 03−4.3000E − 03−4.2000E − 03−4.1000E − 03−4.0692E − 03

−5.2137E − 03−5.2000E − 03−5.1000E − 03−5.0000E − 03−4.9000E − 03−4.8000E − 03−4.7000E − 03−4.6000E − 03−4.5000E − 03−4.4000E − 03−4.3000E − 03−4.2000E − 03−4.1000E − 03−4.0310E − 03

−4.6189E − 03−4.7000E − 03−4.6000E − 03−4.5000E − 03−4.4000E − 03−4.3000E − 03−4.2000E − 03−4.1000E − 03−4.0000E − 03−3.9000E − 03−3.8000E − 03−3.7000E − 03−3.6000E − 03−3.5000E − 03−3.4000E − 03−3.3000E − 03−3.2045E − 03


Vertical displacement/ux Vertical displacement/ux Vertical displacement/uxArch wall height H = 13.2 mArch wall height H = 9.25 mArch wall height H = 5.15 m

Figure 15: Contour maps of the postloading pile cap displacements in each scenario.

Horizontaldisplacement ux

−2.2036E − 02−2.0000E − 02 −1.7500E − 02−1.5000E − 02−1.2500E − 02−1.0000E − 02−7.5000E − 03−5.0000E − 03−2.5000E − 030.0000E + 002.5000E − 035.0000E − 037.5000E − 031.0000E − 021.2500E − 021.5000E − 021.6781E − 02


−2.0000E − 02 −1.7500E − 02−1.5000E − 02−1.2500E − 02−1.0000E − 02−7.5000E − 03−5.0000E − 03−2.5000E − 030.0000E + 002.5000E − 035.0000E − 037.5000E − 031.0000E − 021.2500E − 021.5000E − 021.6837E − 02

−2.0697E − 02−2.0000E − 02 −1.7500E − 02−1.5000E − 02−1.2500E − 02−1.0000E − 02−7.5000E − 03−5.0000E − 03−2.5000E − 030.0000E + 002.5000E − 035.0000E − 037.5000E − 031.0000E − 021.2500E − 021.5000E − 021.6812E − 02

Horizontaldisplacement ux−2.1234E · 02

Figure 16: Patterns of horizontal and vertical displacement transfer after excavation.


−9.2977E − 03−9.0000E − 03−8.5000E − 03−8.0000E − 03−7.5000E − 03−7.0000E − 03−6.5000E − 03−6.0000E − 03−5.5000E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03−3.5000E − 03−3.0000E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 006.1415E − 06



−7.8194E − 03−7.5000E − 03−7.0000E − 03−6.5000E − 03−6.0000E − 03−5.5000E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03

−3.5000E − 03−3.0000E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 001.5406E − 06

−6.8309E − 03−6.5000E − 03−6.0000E − 03−5.5000E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03−3.5000E − 03−3.0000E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 00

Figure 17: Patterns of horizontal and vertical displacement transfer after loading of the pile cap.

14 Complexity

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(b) Arched wall height of 9.25m

Figure 18: Continued.

Complexity 15

case 1case 2case 3

case 4case 5case 6

−8 −2 4 10 16Horizontal Displacement ux (mm)

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(c) Arched wall height of 13.2m

Figure 18: The horizontal displacement of the monitoring point of retaining wall both far away from (left) and adjacent to (right) pilefoundation under the reinforcement of three different height arch walls.

words, the internal compressive stresses of the arched wallare large, which is consistent with the conclusions of ourprevious structural analysis. It is shown that even if the archedwall is buried in complex soil masses, the pressure exertedby the earth on either side of the arched wall will nullifyeach other, and the crown of the arch will bear tremendoushorizontal reactions. Therefore, the horizontal reactions willbe borne by the arched wall, whose stiffness far exceedsthat of the soil masses. Based on the forces at the foot ofthe arch, there is indeed a concentration of stresses aroundthese parts. Nonetheless, these concentrations are not overlysignificant because the forces at the foot of the arch aretransferred to the retaining walls of the foundation pit, whichmay be approximated as being infinite in length. Hence,excessive deformations and stresses will not occur at the footof the arch. However, in actual applications, there is a gapbetween the retaining walls, and the soil masses betweenthe walls cannot effectively transfer the stresses of the archfeet. Therefore, the selection of an appropriate reinforcementscheme for the feet of the arch is necessary. One suchexample is the installation of interlocked isolation piles. Inaddition, the three arched walls have similar distributions indisplacement, as the displacements are always large on thesides of the wall and small in the middle. As the height ofthe arched wall increases, the zone of stress concentration

on either side of the arched wall gradually expands while themaximum stress gradually decreases.

4.3. Analyzing the Reinforcement Effects of Mounting a Row ofInclined Piles under the Pile Cap (3rd Reinforcement Scheme).To improve the ability of the pile cap foundation to resist hor-izontal displacements, we changed a pile-row on the pile capside closer to the foundation pit into inclined piles. Numericalsimulations were then performed to compare inclined pileswith inclinations of 30∘, 45∘, and 60∘. The contour maps ofthe postexcavation and postloading horizontal and verticaldisplacements corresponding to these three cases are shownin Figures 22 and 23. Based on the results of the calcula-tions, the horizontal displacement of the pile cap increasessignificantly after the subway foundation pit was excavated,when the inclinations of the inclined piles were 30∘, 45∘, and60∘. As the overall stiffness of steel supports is lower thanthat of concrete supports, this may have been caused by theweaker deformation resistance of the steel supports. After thepile cap was loaded, the horizontal displacements caused bythe load at the center of the pile cap were 12.60mm (30∘),12.58mm (45∘), and 11.82mm (60∘). Therefore, inclined pileswith an inclination of 60∘ produced the best reinforcementof these piles. Without any reinforcement, the horizontaldisplacement caused by the loading of the pile cap was

16 Complexity

Principal StressesScale: 0.000381348

Minimum Prin

−3.0984E + 03−3.0000E + 03−2.7500E + 03−2.5000E + 03−2.2500E + 03−2.0000E + 03−1.7500E + 03−1.5000E + 03−1.2500E + 03−1.0000E + 03−7.5000E + 02−5.0000E + 02−2.5000E + 020.0000E + 001.2983E + 02

partial enlarged drawing

Figure 19: Contour map of the postexcavation principal stresses in the arched wall.

Principal StressesScale: 0.000112273

Minimum Prin

−8.0757E + 03−8.0000E + 03−7.5000E + 03−7.0000E + 03−6.5000E + 03−6.0000E + 03−5.5000E + 03−5.0000E + 03−4.5000E + 03−4.0000E + 03−3.5000E + 03−2.5000E + 03−2.0000E + 03−1.5000E + 03−1.0000E + 03−5.0000E + 020.0000E + 004.7303E + 01

A topical map of the vault

A topical map of the arch foot

Figure 20: Contour map of the postloading principal stresses in the arched wall.

Horizontal displacement/ux Horizontal displacement/ux Horizontal displacement/ux−9.2977E − 03−9.2000E − 03−9.0000E − 03−8.8000E − 03−8.6000E − 03−8.4000E − 03−8.2000E − 03−8.0000E − 03−7.8000E − 03−7.6000E − 03−7.4000E − 03−7.2000E − 03−7.0000E − 03−6.8287E − 03

−8.1993E − 03−8.0000E − 03−8.0000E − 03−7.8000E − 03−7.6000E − 03−7.4000E − 03−7.2000E − 03−7.0000E − 03−6.8000E − 03−6.6000E − 03−6.4000E − 03−6.2000E − 03−6.0126E − 03


Figure 21: The contour map of postloading displacements corresponding to three different arched wall heights does have a certain level ofeffectiveness in reducing horizontal displacements.

Complexity 17

Horizontal displacement/ux Horizontal displacement/ux Horizontal displacement/ux−7.0874E − 03−7.0000E − 03−6.7500E − 03−6.5000E − 03−6.2500E − 03−6.0000E − 03−5.7500E − 03−5.5000E − 03−5.2500E − 03−5.0000E − 03−4.7500E − 03−4.5000E − 03−4.2500E − 03−4.0000E − 03−3.7500E − 03−3.5000E − 03−3.2500E − 03−3.0000E − 03−2.8726E − 03


−5.5745E − 03−5.5000E − 03−5.2500E − 03−5.0000E − 03−4.7500E − 03−4.5000E − 03−4.2500E − 03−4.0000E − 03−3.7500E − 03−3.5000E − 03−3.2500E − 03−3.0000E − 03−2.9788E − 03

−4.8784E − 03−4.5000E − 03−4.0000E − 03−3.5000E − 03−3.0000E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 005.0000E − 041.0000E − 031.5000E − 031.5284E − 03

Vertical displacement/ux Vertical displacement/ux Vertical displacement/ux−5.0312E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03−3.5000E − 03−3.0000E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 005.0000E − 041.0000E − 031.5000E − 031.7584E − 03

−5.0572E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03−3.5000E − 03−3.0000E − 03−2.5000E − 03−2.0000E − 03−1.5000E − 03−1.0000E − 03−5.0000E − 040.0000E + 005.0000E − 041.0000E − 031.5000E − 032.0000E − 032.2440E − 03

Inclined pile angle 30∘ Inclined pile angle 45∘ Inclined pile angle 60∘

Figure 22: Postexcavation contour maps of pile cap displacements in each case.

Table 4: The effectiveness of each reinforcement scheme in controlling the horizontal displacement of the pile cap.

Horizontaldisplacement

Reinforcement scheme

Withoutreinforcement

Reinforcementvia isolationpiles and

jet-grouted piles

Reinforcement using arched walls withdifferent heights

Setting up inclined piles withdifferent inclinations under the pile

capArched wallheight of5.15m

Arched wallheight of9.25m

Arched wallheight of13.2m

Inclinationof 30∘

Inclination of45∘

Inclinationof 60∘

Postexcavation 3.82 2.92 3.32 4.23 4.41 2.93 3.21 3.05Postloading 14.8 6.03 8.94 7.42 6.44 12.60 12.58 11.82

14.80mm. Hence, the use of inclined piles with an inclinationof 60∘ reduces the horizontal displacement of the pile cap by3mm; therefore, the inclined piles have a significant effecton controlling horizontal displacement. However, when theinclination of the inclined piles was 60∘, the projection ofthe pile onto the vertical axis is only half the length of avertical pile. Therefore, if the elevation of the bottom endof the inclined piles is maintained at the same level as thatof a vertical pile, the suppression of horizontal displacementusing inclined piles could be more effective. In summary, thisscheme does have a certain level of effectiveness in reducinghorizontal displacements.

4.4. Comparison of the Effectiveness of Each ReinforcementScheme in Controlling the Horizontal Displacements of a PileCap. The deformations of the skewed arch pile foundationsfollowing the application of each reinforcement scheme areshown in Table 4 to facilitate a comparative analysis. Thecombination of isolation piles and jet-grouted piles is themost effective scheme for limiting horizontal displacements

in the skewed arch piles. However, this reinforcement schemealso involves tremendous costs. The arched wall reinforce-ment scheme is also effective at restricting the horizontaldisplacements of the piles, and a 13m high arched wall issufficient for achieving excellent results from this aspect. Theuse of inclined piles under the pile cap also limits horizontaldisplacements to an extent, but it is not a particularly effectivemethod because the reduction in horizontal displacementwas only ∼2mm. Hence, the use of inclined piles alone isinsufficient formeeting the needs of engineering applications.In summary, the archedwall reinforcement scheme is the bestof the three aforementioned schemes in terms of horizontaldisplacement control and project costs. Furthermore, thestress states of the arched wall will make full use of an archedstructure’s advantages.

5. Conclusions

To study the interactions between deep foundation pits andthe pile foundations of skewed arches, we have performed

18 Complexity


−1.2840E − 02−1.2500E − 02−1.2000E − 02−1.1500E − 02−1.1000E − 02−1.0500E − 02−1.0000E − 02−9.5000E − 03−9.0000E − 03−8.5000E − 03−8.0000E − 03−7.5000E − 03−7.0000E − 03−6.5000E − 03−6.0182E − 03


−1.2053E − 02−1.2000E − 02−1.1500E − 02−1.1000E − 02−1.0500E − 02−1.0000E − 02−9.5000E − 03−9.0000E − 03−8.5000E − 03−8.0000E − 03−7.5000E − 03−7.0000E − 03−6.5000E − 03−6.0700E − 03

−1.0628E − 02−1.0500E − 02−1.0000E − 02−9.5000E − 03−9.0000E − 03−8.5000E − 03−7.5000E − 03−7.0000E − 03−6.5000E − 03−6.0000E − 03−5.5000E − 03−5.0000E − 03−4.5000E − 03−4.0074E − 03


−1.0121E − 02−1.0000E − 02−9.5000E − 03−9.0000E − 03−8.5000E − 03−7.5000E − 03−7.0000E − 03−6.5000E − 03−6.0000E − 03−5.5000E − 03−5.0000E − 03−4.5000E − 03−4.0000E − 03−3.8180E − 03


Inclined pile angle 30∘ Inclined pile angle 45∘ Inclined pile angle 60∘

Figure 23: Postloading contour maps of pile cap displacements in each case.

computational analyses on the displacement responses ofpile caps and foundation pit retaining walls, which accountfor a variety of construction scenarios and reinforcementschemes. The computational results indicate that the mag-nitude of horizontal displacements at the top of the pilefoundations is strongly affected by the soil modulus of theupper soils. The mechanisms by which a deep foundation pitinteracted with its adjacent pile foundations were revealed.The excavation of deep foundation pits causes the soil massesin its surroundings to move towards the foundation pit,and displacements occur in nearby skewed arch piles, asthey lie within the range of influence of the foundation pit.The excavation of the foundation pit effectively underminesthe lateral constraints of the skewed arch pile foundations,thus reducing the bearing capacities of the piles to a certainextent. The ground stresses induced by the loading of theskewed arch piles are dispersed within the soil mass, whichultimately leads to the application of additional stresses on theretainingwalls of the foundation pit.These additional stressesshould be accounted for during the design of the retainingwall structures of the foundation pit. Three techniques forcontrolling the deformations were considered. The first ofthese techniques is the use of isolation piles and jet-groutedpiles in the upper gravel layer of the soil mass.This techniqueensures that deep foundation pits can be constructed safely,mitigates the effects of foundation pit excavation on nearbyskewed arch pile foundations, and satisfies the displacementcontrol requirements of skewed arch pile caps. The secondtechnique is a novel archedwall-based reinforcement scheme.The third technique involves the installation of a single rowof inclined piles under the pile cap, based on the fact that the

piles of a skewed arch are primarily subjected to horizontalloads. The effects of these reinforcement schemes were thencompared. The arched wall reinforcement scheme was foundto deliver the best outcomes. Furthermore, the stress statesof the arched wall made full use of the arched structure’sadvantages. The findings of this study can be directly appliedin the construction and design of subway foundation pits.

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper.

Acknowledgments

This work was supported by the National Natural ScienceFoundation of China (Grant no. 41572245).

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